Arithmetic Progression Worksheet for Olympiad

Maths Olympiad topic 29: Sequences and AP · Set 491 · 40 questions

How to solve it (Same step every time): In an AP the gap (common difference d) is always the same. nth term = a + (n − 1) × d, where a is the first term. Sum of n terms = n × (first + last) ÷ 2; so 1 + 2 + … + n = n × (n + 1) ÷ 2, and the first n odd numbers add up to n × n.

1. 1.What is the sum of the first 7 terms of the AP 2, 7, 12, …? (a) 238 (b) 32 (c) 119 (d) 124
2. 2.What is the sum of the first 12 terms of the AP 2, 8, 14, …? (a) 456 (b) 68 (c) 420 (d) 840
3. 3.What is the sum of all the whole numbers from 1 to 33? (a) 561 (b) 528 (c) 562 (d) 1122
4. 4.What is the 16th term of the AP 18, 25, 32, 39, …? (a) 105 (b) 123 (c) 112 (d) 130
5. 5.What is the sum of the first 7 terms of the AP 6, 7, 8, …? (a) 126 (b) 12 (c) 64 (d) 63
6. 6.What is the sum of all the whole numbers from 1 to 10? (a) 55 (b) 50 (c) 110 (d) 45
7. 7.What is the 17th term of the AP 1, 8, 15, 22, …? (a) 112 (b) 120 (c) 119 (d) 113
8. 8.What is the sum of all the whole numbers from 1 to 21? (a) 231 (b) 462 (c) 232 (d) 210
9. 9.What is the 18th term of the AP 2, 7, 12, 17, …? (a) 92 (b) 90 (c) 85 (d) 87
10. 10.What is the 16th term of the AP 19, 23, 27, 31, …? (a) 83 (b) 60 (c) 64 (d) 79
11. 11.Which term of the AP 19, 23, 27, 31, … is 103? (a) 23rd (b) 24th (c) 22nd (d) 21st
12. 12.What is the 13th term of the AP 8, 13, 18, 23, …? (a) 65 (b) 68 (c) 73 (d) 60
13. 13.What is the 24th term of the AP 4, 7, 10, 13, …? (a) 73 (b) 69 (c) 76 (d) 72
14. 14.What is the 23rd term of the AP 12, 14, 16, 18, …? (a) 56 (b) 44 (c) 58 (d) 46
15. 15.What is the sum of all the whole numbers from 1 to 24? (a) 600 (b) 300 (c) 288 (d) 276
16. 16.What is the sum of the first 8 terms of the AP 5, 11, 17, …? (a) 416 (b) 47 (c) 232 (d) 208
17. 17.What is the missing term in the AP 11, 18, 25, ?, 39? (a) 32 (b) 39 (c) 31 (d) 33
18. 18.What is the missing term in the AP 14, ?, 24, 29, 34? (a) 24 (b) 20 (c) 18 (d) 19
19. 19.What is the 19th term of the AP 12, 16, 20, 24, …? (a) 72 (b) 84 (c) 76 (d) 88
20. 20.What is the sum of the first 30 odd numbers (1 + 3 + 5 + …)? (a) 930 (b) 59 (c) 900 (d) 465
21. 21.What is the missing term in the AP 7, ?, 17, 22, 27? (a) 17 (b) 11 (c) 13 (d) 12
22. 22.What is the 16th term of the AP 14, 20, 26, 32, …? (a) 90 (b) 110 (c) 104 (d) 96
23. 23.What is the missing term in the AP 9, 15, 21, ?, 33? (a) 26 (b) 28 (c) 33 (d) 27
24. 24.What is the 14th term of the AP 10, 15, 20, 25, …? (a) 75 (b) 65 (c) 70 (d) 80
25. 25.What is the 10th term of the AP 3, 11, 19, 27, …? (a) 80 (b) 75 (c) 72 (d) 83
26. 26.Which term of the AP 6, 13, 20, 27, … is 181? (a) 25th (b) 28th (c) 26th (d) 27th
27. 27.What is the 28th term of the AP 20, 28, 36, 44, …? (a) 236 (b) 216 (c) 224 (d) 244
28. 28.Which term of the AP 15, 21, 27, 33, … is 213? (a) 36th (b) 35th (c) 34th (d) 33rd
29. 29.What is the missing term in the AP 18, 27, ?, 45, 54? (a) 35 (b) 45 (c) 36 (d) 37
30. 30.What is the 16th term of the AP 17, 26, 35, 44, …? (a) 135 (b) 161 (c) 144 (d) 152
31. 31.What is the 39th term of the AP 11, 13, 15, 17, …? (a) 76 (b) 89 (c) 78 (d) 87
32. 32.What is the 12th term of the AP 11, 15, 19, 23, …? (a) 59 (b) 44 (c) 55 (d) 48
33. 33.What is the sum of the first 6 terms of the AP 2, 5, 8, …? (a) 66 (b) 17 (c) 57 (d) 114
34. 34.What is the sum of the first 9 terms of the AP 8, 9, 10, …? (a) 216 (b) 16 (c) 109 (d) 108
35. 35.What is the 24th term of the AP 6, 11, 16, 21, …? (a) 126 (b) 121 (c) 120 (d) 115
36. 36.What is the 33rd term of the AP 10, 12, 14, 16, …? (a) 76 (b) 66 (c) 64 (d) 74
37. 37.What is the missing term in the AP 7, ?, 19, 25, 31? (a) 19 (b) 13 (c) 14 (d) 12
38. 38.What is the missing term in the AP 16, ?, 28, 34, 40? (a) 28 (b) 21 (c) 22 (d) 23
39. 39.What is the sum of the first 11 terms of the AP 4, 8, 12, …? (a) 286 (b) 264 (c) 44 (d) 528
40. 40.What is the 19th term of the AP 5, 8, 11, 14, …? (a) 57 (b) 62 (c) 59 (d) 54

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad